Dynamical density-matrix renormalization-group method

By E. Jeckelmann. 2002

289 citations recorded by the source corpus.

A density-matrix renormalization-group (DMRG) method for calculating dynamical properties and excited states in low-dimensional lattice quantum many-body systems is presented. The method is based on an exact variational principle for dynamical correlation functions and the excited states contributing to them. This dynamical DMRG is an alternate formulation of the correction vector DMRG but is both simpler and more accurate. The finite-size scaling of spectral functions is discussed and a method for analyzing the scaling of dense spectra is described. The key idea of the method is a size-dependent broadening of the spectrum. The dynamical DMRG and the finite-size scaling analysis are demonstrated on the optical conductivity of the one-dimensional Peierls-Hubbard model. Comparisons with analytical results show that the spectral functions of infinite systems can be reproduced almost exactly with these techniques. The optical conductivity of the Mott-Peierls insulator is investigated and it is shown that its spectrum is qualitatively different from the simple spectra observed in Peierls (band) insulators and one-dimensional Mott-Hubbard insulators.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/68ff3322a07b0a33970b50708ec6cdd72d82d0ef

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Low-rank solvers for unsteady Stokes–Brinkman optimal control problem with random data (2016, unknown): “In quantum physics, a powerful realization of the alternation idea is the Density Matrix Renormalization Group (DMRG) algorithm [54], which is mainly used for eigenvalue problems, but also for linear systems [24].”
Tensor Ring Decomposition (2016, background): “…large-scale problems in numerical analysis, which includes the optimization of Rayleigh quotient, e.g., density matrix renormalization group (DMRG) [37], [38], the eigenvalue or singular value problem [39], [40], and the approximate solution of linear systems, e.g., alternating minimal energy…”
ALTERNATING MINIMAL ENERGY METHODS FOR LINEAR SYSTEMS IN HIGHER DIMENSIONS∗ (2014, methodology): “1) over MPS vectors was first introduced as the dynamical DMRG [27]; see also the reviews on other MPS/DMRG techniques [53, 54, 25].”
Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions (2013, unknown): “1) over MPS vectors was first introduced as the dynamical DMRG [27]; see also the reviews on other MPS/DMRG techniques [53, 54, 25].”
The mass spectrum of the Schwinger model with matrix product states (2013, methodology): “This route was first explored using the original DMRG formulation [20, 21].”